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A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twenty-fourth of its capacity, during the second hour at one-twelfth of its capacity, during the third hour at one-eighth of its usual capacity, during the fourth hours at one-fourth of its usual capacity and during the fifth hour it was only one-half as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank a constant rate, the empty cistern could be filled in 5 hours, all the three pipe working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time?

A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twenty-fourth of its capacity, during the second hour at one-twelfth of its capacity, during the third hour at one-eighth of its usual capacity, during the fourth hours at one-fourth of its usual capacity and during the fifth hour it was only one-half as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank a constant rate, the empty cistern could be filled in 5 hours, all the three pipe working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time? Correct Answer 10

1st pipe can fill an empty cistern in = 1 hour

⇒ In 1 hour 1st pipe can fill = 1

2nd pipe can fill an empty cistern in = 2 hours

⇒ In 2 hours 2nd pipe can fill = 2

Let in 1 hour drain pipe can empty = x

According to problem,

⇒ (1/24 + 1/12 + 1/8 + 1/4 + 1/2) + 1/2(1/24 + 1/12 + 1/8 + 1/4 + 1/2) – 5x = 1

⇒ (1 + 2 + 3 + 6 + 12) /24 + 1/2 × (1 + 2 + 3 + 6 + 12) /24 – 5x = 1

⇒ 1 + 1/2 – 5x = 1

⇒ 5x = 1/2

⇒ x = 1/10

∴ In 1 hour drain pipe can empty = 1/10

∴ The drain pipe can empty the tank in = 10 hours

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